In this picture the tile is already off, but you can see that the underlayment by the tub and toilet is all rotted out already. The subfloor is also weakened by the water, but seemed sturdy enough not to go through hassle of pulling it all up.

Old toilet was the hardest part. I eventually gave up trying to cut the bolts off myself (after 10 hours of trying, & many broken "diamond" Dremel blades, no joke!). A plumber with a saws-all was able to do it in 10 minutes.
The plastic cap over the toilet hole (flange) is the new wax seal, I put it on to keep out the sewer gases.
Note the extra rot around the toilet. I put two layers of luon down around the toilet with little pegs to further support the flange (later on).

I put down a layer of luon (1/4 inch plywood) throughout the bathroom. I put two lawyers down by the toilet. It was still level with the rest of the bathroom. If this wouldn't work for you, you may want to put down luon and maybe 1/4 or 1/2 inch plywood under that for support.
Note that I had to cut the plywood in half to slide under the flange. It was an old lead model and it would have been difficult to replace. I also had to do creative cutting for the valves and because the walls were not square.

After sanding and filling in cracks w/ sealant made for this purpose, I had a clean (dry) floor ready for the linoleum.

We wanted to put down real linoleum (made from flaxseed, etc), but it was unavailable so we went with vinyl linoleum.
We didn't like tile (although it would've been EASIER to lay down), because it is hard and very cold.
You CANNOT use vinyl *tile*, because it is a bathroom floor and water will seep through the edges between tiles.
We laid down one sheet of Vinyl we cut to fit the bathroom. This required alot of measuring, especially around corners. We cut the sheet vinyl in the basement where there was a lot of room.

To make the vinyl stick we laid the pre-cut sheet down, then rolled it up one side at a time and added the right amount of glue (epoxy, whatever you call it). We then rolled it (we didn't want to buy roller, so just used large heavy class jar) for about an hour to get rid of air bubbles.

Ta-Da. Note the caulking around the tub (an essential step- easy if done quickly (before it gets hard) and fully the first time).

This wasn't the end b/c the toilet still gave me problems. It continued to leak profusely and required ALOT of fine tuning (~3 hours and alot of stress). As I said earlier, the toilet was the hardest part.

BTW, this floor has kept looking great, and without leaks, coming up, or too much wear, for 6 months now already.